Ratio and Proportion Competitive Exams
100 questions · Mathematics
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Question 1 of 100
If 27 men can do a work in 30 days, in how many days will 54 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 27×30 = 54×D2 => D2 = 15 days.
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Question 2 of 100
Divide Rs. 252 in the ratio 4:3. What is the first part?
ExplanationTotal parts = 4+3 = 7. First part = 252 × (4/7) = 144.
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Question 3 of 100
If A:B = 5:5 and B:C = 5:5, find A:B:C.
ExplanationSince B is common and equal (5) in both ratios, A:B:C = 5:5:5.
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Question 4 of 100
Find the fourth proportional to 5, 7, and 8.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (7×8)/5 = 11.20.
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Question 5 of 100
Simplify the ratio 40:20.
ExplanationDivide both sides by HCF 20. 40/20 : 20/20 = 2:1.
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Question 6 of 100
If A:B = 5:4 and B:C = 4:6, find A:B:C.
ExplanationSince B is common and equal (4) in both ratios, A:B:C = 5:4:6.
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Question 7 of 100
Find the mean proportional between 16 and 49.
ExplanationMean proportional between x and y is √(xy). √(16 × 49) = 28.
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Question 8 of 100
A mixture contains milk and water in the ratio 7:5. If there is 21 liters of milk, how much water is there?
ExplanationRatio is 7:5. Let common multiple be x. 7x = 21 => x = 3. Water = 5x = 15 liters.
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Question 9 of 100
Find the third proportional to 6 and 2.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 4/6 = 0.67.
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Question 10 of 100
A mixture contains milk and water in the ratio 2:3. If there is 6 liters of milk, how much water is there?
ExplanationRatio is 2:3. Let common multiple be x. 2x = 6 => x = 3. Water = 3x = 9 liters.
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Question 11 of 100
Two numbers are in the ratio 4:2. If their sum is 18, what is the first number?
ExplanationSum of parts = 6. First number = 18 × (4/6) = 12.
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Question 12 of 100
Price of item A is 13 and B is 19. If their quantities are in ratio 5:4, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (5×13) : (4×19) = 65:76. Simplify if needed.
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Question 13 of 100
If A:B = 8:4 and B:C = 4:5, find A:B:C.
ExplanationSince B is common and equal (4) in both ratios, A:B:C = 8:4:5.
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Question 14 of 100
If 22 men can do a work in 22 days, in how many days will 44 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 22×22 = 44×D2 => D2 = 11 days.
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Question 15 of 100
A mixture contains milk and water in the ratio 4:5. If there is 24 liters of milk, how much water is there?
ExplanationRatio is 4:5. Let common multiple be x. 4x = 24 => x = 6. Water = 5x = 30 liters.
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Question 16 of 100
Find the fourth proportional to 8, 2, and 2.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (2×2)/8 = 0.50.
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Question 17 of 100
Find the third proportional to 6 and 6.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 36/6 = 6.00.
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Question 18 of 100
Find the fourth proportional to 7, 5, and 7.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (5×7)/7 = 5.00.
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Question 19 of 100
Two numbers are in the ratio 5:4. If their sum is 27, what is the first number?
ExplanationSum of parts = 9. First number = 27 × (5/9) = 15.
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Question 20 of 100
Two numbers are in the ratio 3:4. If their sum is 35, what is the first number?
ExplanationSum of parts = 7. First number = 35 × (3/7) = 15.
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Question 21 of 100
A mixture contains milk and water in the ratio 4:5. If there is 8 liters of milk, how much water is there?
ExplanationRatio is 4:5. Let common multiple be x. 4x = 8 => x = 2. Water = 5x = 10 liters.
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Question 22 of 100
Find the third proportional to 7 and 4.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 16/7 = 2.29.
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Question 23 of 100
Divide Rs. 162 in the ratio 2:4. What is the first part?
ExplanationTotal parts = 2+4 = 6. First part = 162 × (2/6) = 54.
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Question 24 of 100
If A:B = 5:3 and B:C = 3:6, find A:B:C.
ExplanationSince B is common and equal (3) in both ratios, A:B:C = 5:3:6.
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Question 25 of 100
Find the third proportional to 5 and 3.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 9/5 = 1.80.
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Question 26 of 100
Price of item A is 30 and B is 19. If their quantities are in ratio 2:4, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (2×30) : (4×19) = 60:76. Simplify if needed.
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Question 27 of 100
Simplify the ratio 25:40.
ExplanationDivide both sides by HCF 5. 25/5 : 40/5 = 5:8.
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Question 28 of 100
A mixture contains milk and water in the ratio 2:2. If there is 14 liters of milk, how much water is there?
ExplanationRatio is 2:2. Let common multiple be x. 2x = 14 => x = 7. Water = 2x = 14 liters.
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Question 29 of 100
Find the mean proportional between 36 and 100.
ExplanationMean proportional between x and y is √(xy). √(36 × 100) = 60.
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Question 30 of 100
Price of item A is 14 and B is 40. If their quantities are in ratio 5:3, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (5×14) : (3×40) = 70:120. Simplify if needed.
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Question 31 of 100
Find the fourth proportional to 6, 9, and 10.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (9×10)/6 = 15.00.
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Question 32 of 100
Find the third proportional to 6 and 4.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 16/6 = 2.67.
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Question 33 of 100
Find the fourth proportional to 2, 4, and 5.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (4×5)/2 = 10.00.
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Question 34 of 100
If 28 men can do a work in 28 days, in how many days will 56 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 28×28 = 56×D2 => D2 = 14 days.
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Question 35 of 100
Price of item A is 44 and B is 32. If their quantities are in ratio 2:4, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (2×44) : (4×32) = 88:128. Simplify if needed.
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Question 36 of 100
Two numbers are in the ratio 2:1. If their sum is 27, what is the first number?
ExplanationSum of parts = 3. First number = 27 × (2/3) = 18.
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Question 37 of 100
Price of item A is 48 and B is 32. If their quantities are in ratio 2:4, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (2×48) : (4×32) = 96:128. Simplify if needed.
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Question 38 of 100
Simplify the ratio 30:15.
ExplanationDivide both sides by HCF 15. 30/15 : 15/15 = 2:1.
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Question 39 of 100
Find the fourth proportional to 4, 3, and 6.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (3×6)/4 = 4.50.
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Question 40 of 100
Find the mean proportional between 25 and 100.
ExplanationMean proportional between x and y is √(xy). √(25 × 100) = 50.
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Question 41 of 100
If A:B = 4:5 and B:C = 5:6, find A:B:C.
ExplanationSince B is common and equal (5) in both ratios, A:B:C = 4:5:6.
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Question 42 of 100
Two numbers are in the ratio 4:2. If their sum is 60, what is the first number?
ExplanationSum of parts = 6. First number = 60 × (4/6) = 40.
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Question 43 of 100
If A:B = 6:3 and B:C = 3:2, find A:B:C.
ExplanationSince B is common and equal (3) in both ratios, A:B:C = 6:3:2.
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Question 44 of 100
Divide Rs. 460 in the ratio 1:3. What is the first part?
ExplanationTotal parts = 1+3 = 4. First part = 460 × (1/4) = 115.
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Question 45 of 100
Two numbers are in the ratio 1:1. If their sum is 20, what is the first number?
ExplanationSum of parts = 2. First number = 20 × (1/2) = 10.
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Question 46 of 100
Two numbers are in the ratio 5:3. If their sum is 48, what is the first number?
ExplanationSum of parts = 8. First number = 48 × (5/8) = 30.
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Question 47 of 100
Find the mean proportional between 16 and 25.
ExplanationMean proportional between x and y is √(xy). √(16 × 25) = 20.
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Question 48 of 100
Find the fourth proportional to 4, 8, and 2.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (8×2)/4 = 4.00.
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Question 49 of 100
Divide Rs. 369 in the ratio 2:1. What is the first part?
ExplanationTotal parts = 2+1 = 3. First part = 369 × (2/3) = 246.
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Question 50 of 100
Find the third proportional to 2 and 7.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 49/2 = 24.50.
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Question 51 of 100
Find the fourth proportional to 8, 5, and 7.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (5×7)/8 = 4.38.
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Question 52 of 100
Find the mean proportional between 9 and 25.
ExplanationMean proportional between x and y is √(xy). √(9 × 25) = 15.
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Question 53 of 100
Divide Rs. 300 in the ratio 3:3. What is the first part?
ExplanationTotal parts = 3+3 = 6. First part = 300 × (3/6) = 150.
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Question 54 of 100
Find the third proportional to 4 and 7.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 49/4 = 12.25.
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Question 55 of 100
If A:B = 2:2 and B:C = 2:6, find A:B:C.
ExplanationSince B is common and equal (2) in both ratios, A:B:C = 2:2:6.
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Question 56 of 100
A mixture contains milk and water in the ratio 5:2. If there is 20 liters of milk, how much water is there?
ExplanationRatio is 5:2. Let common multiple be x. 5x = 20 => x = 4. Water = 2x = 8 liters.
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Question 57 of 100
If 12 men can do a work in 24 days, in how many days will 24 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 12×24 = 24×D2 => D2 = 12 days.
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Question 58 of 100
Two numbers are in the ratio 2:2. If their sum is 36, what is the first number?
ExplanationSum of parts = 4. First number = 36 × (2/4) = 18.
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Question 59 of 100
Simplify the ratio 15:15.
ExplanationDivide both sides by HCF 15. 15/15 : 15/15 = 1:1.
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Question 60 of 100
Divide Rs. 480 in the ratio 3:3. What is the first part?
ExplanationTotal parts = 3+3 = 6. First part = 480 × (3/6) = 240.
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Question 61 of 100
Find the fourth proportional to 7, 3, and 2.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (3×2)/7 = 0.86.
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Question 62 of 100
Find the third proportional to 5 and 8.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 64/5 = 12.80.
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Question 63 of 100
Simplify the ratio 40:30.
ExplanationDivide both sides by HCF 10. 40/10 : 30/10 = 4:3.
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Question 64 of 100
Two numbers are in the ratio 2:1. If their sum is 9, what is the first number?
ExplanationSum of parts = 3. First number = 9 × (2/3) = 6.
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Question 65 of 100
A mixture contains milk and water in the ratio 4:3. If there is 8 liters of milk, how much water is there?
ExplanationRatio is 4:3. Let common multiple be x. 4x = 8 => x = 2. Water = 3x = 6 liters.
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Question 66 of 100
Find the mean proportional between 64 and 100.
ExplanationMean proportional between x and y is √(xy). √(64 × 100) = 80.
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Question 67 of 100
Find the third proportional to 5 and 5.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 25/5 = 5.00.
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Question 68 of 100
Find the fourth proportional to 3, 2, and 2.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (2×2)/3 = 1.33.
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Question 69 of 100
Find the mean proportional between 25 and 36.
ExplanationMean proportional between x and y is √(xy). √(25 × 36) = 30.
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Question 70 of 100
Simplify the ratio 36:48.
ExplanationDivide both sides by HCF 12. 36/12 : 48/12 = 3:4.
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Question 71 of 100
Find the mean proportional between 36 and 9.
ExplanationMean proportional between x and y is √(xy). √(36 × 9) = 18.
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Question 72 of 100
Divide Rs. 231 in the ratio 4:3. What is the first part?
ExplanationTotal parts = 4+3 = 7. First part = 231 × (4/7) = 132.
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Question 73 of 100
If A:B = 6:5 and B:C = 5:4, find A:B:C.
ExplanationSince B is common and equal (5) in both ratios, A:B:C = 6:5:4.
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Question 74 of 100
A mixture contains milk and water in the ratio 3:4. If there is 6 liters of milk, how much water is there?
ExplanationRatio is 3:4. Let common multiple be x. 3x = 6 => x = 2. Water = 4x = 8 liters.
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Question 75 of 100
If 18 men can do a work in 18 days, in how many days will 36 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 18×18 = 36×D2 => D2 = 9 days.
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Question 76 of 100
Price of item A is 39 and B is 19. If their quantities are in ratio 3:5, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (3×39) : (5×19) = 117:95. Simplify if needed.
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Question 77 of 100
Divide Rs. 130 in the ratio 1:4. What is the first part?
ExplanationTotal parts = 1+4 = 5. First part = 130 × (1/5) = 26.
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Question 78 of 100
If 10 men can do a work in 28 days, in how many days will 20 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 10×28 = 20×D2 => D2 = 14 days.
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Question 79 of 100
If A:B = 6:6 and B:C = 6:3, find A:B:C.
ExplanationSince B is common and equal (6) in both ratios, A:B:C = 6:6:3.
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Question 80 of 100
Price of item A is 17 and B is 35. If their quantities are in ratio 5:2, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (5×17) : (2×35) = 85:70. Simplify if needed.
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Question 81 of 100
Price of item A is 32 and B is 46. If their quantities are in ratio 2:5, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (2×32) : (5×46) = 64:230. Simplify if needed.
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Question 82 of 100
If 22 men can do a work in 14 days, in how many days will 44 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 22×14 = 44×D2 => D2 = 7 days.
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Question 83 of 100
If A:B = 3:4 and B:C = 4:3, find A:B:C.
ExplanationSince B is common and equal (4) in both ratios, A:B:C = 3:4:3.
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Question 84 of 100
Price of item A is 20 and B is 39. If their quantities are in ratio 2:5, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (2×20) : (5×39) = 40:195. Simplify if needed.
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Question 85 of 100
Find the third proportional to 2 and 8.
ExplanationThird proportional c satisfies a:b = b:c. So c = b²/a = 64/2 = 32.00.
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Question 86 of 100
Find the mean proportional between 49 and 9.
ExplanationMean proportional between x and y is √(xy). √(49 × 9) = 21.
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Question 87 of 100
Find the mean proportional between 4 and 81.
ExplanationMean proportional between x and y is √(xy). √(4 × 81) = 18.
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Question 88 of 100
A mixture contains milk and water in the ratio 2:3. If there is 16 liters of milk, how much water is there?
ExplanationRatio is 2:3. Let common multiple be x. 2x = 16 => x = 8. Water = 3x = 24 liters.
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Question 89 of 100
Divide Rs. 260 in the ratio 4:4. What is the first part?
ExplanationTotal parts = 4+4 = 8. First part = 260 × (4/8) = 130.
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Question 90 of 100
If 29 men can do a work in 14 days, in how many days will 58 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 29×14 = 58×D2 => D2 = 7 days.
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Question 91 of 100
Divide Rs. 432 in the ratio 4:2. What is the first part?
ExplanationTotal parts = 4+2 = 6. First part = 432 × (4/6) = 288.
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Question 92 of 100
Simplify the ratio 50:45.
ExplanationDivide both sides by HCF 5. 50/5 : 45/5 = 10:9.
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Question 93 of 100
Two numbers are in the ratio 3:3. If their sum is 48, what is the first number?
ExplanationSum of parts = 6. First number = 48 × (3/6) = 24.
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Question 94 of 100
If 13 men can do a work in 12 days, in how many days will 26 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 13×12 = 26×D2 => D2 = 6 days.
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Question 95 of 100
A mixture contains milk and water in the ratio 5:5. If there is 25 liters of milk, how much water is there?
ExplanationRatio is 5:5. Let common multiple be x. 5x = 25 => x = 5. Water = 5x = 25 liters.
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Question 96 of 100
Price of item A is 46 and B is 16. If their quantities are in ratio 5:4, what is the ratio of their total costs?
ExplanationTotal cost = Price × Quantity. Cost ratio = (5×46) : (4×16) = 230:64. Simplify if needed.
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Question 97 of 100
Simplify the ratio 50:50.
ExplanationDivide both sides by HCF 50. 50/50 : 50/50 = 1:1.
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Question 98 of 100
If 30 men can do a work in 20 days, in how many days will 60 men do the same work?
ExplanationMore men, less days (Inverse proportion). M1×D1 = M2×D2 => 30×20 = 60×D2 => D2 = 10 days.
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Question 99 of 100
Find the fourth proportional to 7, 2, and 7.
ExplanationFourth proportional d satisfies a:b = c:d. So d = (b×c)/a = (2×7)/7 = 2.00.
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Question 100 of 100
Simplify the ratio 40:10.
ExplanationDivide both sides by HCF 10. 40/10 : 10/10 = 4:1.
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